/usr/lib/python3/dist-packages/shapely/affinity.py is in python3-shapely 1.6.4-1.
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from math import sin, cos, tan, pi
__all__ = ['affine_transform', 'rotate', 'scale', 'skew', 'translate']
def affine_transform(geom, matrix):
"""Returns a transformed geometry using an affine transformation matrix.
The coefficient matrix is provided as a list or tuple with 6 or 12 items
for 2D or 3D transformations, respectively.
For 2D affine transformations, the 6 parameter matrix is::
[a, b, d, e, xoff, yoff]
which represents the augmented matrix::
/ a b xoff \
[x' y' 1] = [x y 1] | d e yoff |
\ 0 0 1 /
or the equations for the transformed coordinates::
x' = a * x + b * y + xoff
y' = d * x + e * y + yoff
For 3D affine transformations, the 12 parameter matrix is::
[a, b, c, d, e, f, g, h, i, xoff, yoff, zoff]
which represents the augmented matrix::
/ a b c xoff \
[x' y' z' 1] = [x y z 1] | d e f yoff |
| g h i zoff |
\ 0 0 0 1 /
or the equations for the transformed coordinates::
x' = a * x + b * y + c * z + xoff
y' = d * x + e * y + f * z + yoff
z' = g * x + h * y + i * z + zoff
"""
if geom.is_empty:
return geom
if len(matrix) == 6:
ndim = 2
a, b, d, e, xoff, yoff = matrix
if geom.has_z:
ndim = 3
i = 1.0
c = f = g = h = zoff = 0.0
matrix = a, b, c, d, e, f, g, h, i, xoff, yoff, zoff
elif len(matrix) == 12:
ndim = 3
a, b, c, d, e, f, g, h, i, xoff, yoff, zoff = matrix
if not geom.has_z:
ndim = 2
matrix = a, b, d, e, xoff, yoff
else:
raise ValueError("'matrix' expects either 6 or 12 coefficients")
def affine_pts(pts):
"""Internal function to yield affine transform of coordinate tuples"""
if ndim == 2:
for x, y in pts:
xp = a * x + b * y + xoff
yp = d * x + e * y + yoff
yield (xp, yp)
elif ndim == 3:
for x, y, z in pts:
xp = a * x + b * y + c * z + xoff
yp = d * x + e * y + f * z + yoff
zp = g * x + h * y + i * z + zoff
yield (xp, yp, zp)
# Process coordinates from each supported geometry type
if geom.type in ('Point', 'LineString', 'LinearRing'):
return type(geom)(list(affine_pts(geom.coords)))
elif geom.type == 'Polygon':
ring = geom.exterior
shell = type(ring)(list(affine_pts(ring.coords)))
holes = list(geom.interiors)
for pos, ring in enumerate(holes):
holes[pos] = type(ring)(list(affine_pts(ring.coords)))
return type(geom)(shell, holes)
elif geom.type.startswith('Multi') or geom.type == 'GeometryCollection':
# Recursive call
# TODO: fix GeometryCollection constructor
return type(geom)([affine_transform(part, matrix)
for part in geom.geoms])
else:
raise ValueError('Type %r not recognized' % geom.type)
def interpret_origin(geom, origin, ndim):
"""Returns interpreted coordinate tuple for origin parameter.
This is a helper function for other transform functions.
The point of origin can be a keyword 'center' for the 2D bounding box
center, 'centroid' for the geometry's 2D centroid, a Point object or a
coordinate tuple (x0, y0, z0).
"""
# get coordinate tuple from 'origin' from keyword or Point type
if origin == 'center':
# bounding box center
minx, miny, maxx, maxy = geom.bounds
origin = ((maxx + minx)/2.0, (maxy + miny)/2.0)
elif origin == 'centroid':
origin = geom.centroid.coords[0]
elif isinstance(origin, str):
raise ValueError("'origin' keyword %r is not recognized" % origin)
elif hasattr(origin, 'type') and origin.type == 'Point':
origin = origin.coords[0]
# origin should now be tuple-like
if len(origin) not in (2, 3):
raise ValueError("Expected number of items in 'origin' to be "
"either 2 or 3")
if ndim == 2:
return origin[0:2]
else: # 3D coordinate
if len(origin) == 2:
return origin + (0.0,)
else:
return origin
def rotate(geom, angle, origin='center', use_radians=False):
"""Returns a rotated geometry on a 2D plane.
The angle of rotation can be specified in either degrees (default) or
radians by setting ``use_radians=True``. Positive angles are
counter-clockwise and negative are clockwise rotations.
The point of origin can be a keyword 'center' for the bounding box
center (default), 'centroid' for the geometry's centroid, a Point object
or a coordinate tuple (x0, y0).
The affine transformation matrix for 2D rotation is:
/ cos(r) -sin(r) xoff \
| sin(r) cos(r) yoff |
\ 0 0 1 /
where the offsets are calculated from the origin Point(x0, y0):
xoff = x0 - x0 * cos(r) + y0 * sin(r)
yoff = y0 - x0 * sin(r) - y0 * cos(r)
"""
if not use_radians: # convert from degrees
angle *= pi/180.0
cosp = cos(angle)
sinp = sin(angle)
if abs(cosp) < 2.5e-16:
cosp = 0.0
if abs(sinp) < 2.5e-16:
sinp = 0.0
x0, y0 = interpret_origin(geom, origin, 2)
matrix = (cosp, -sinp, 0.0,
sinp, cosp, 0.0,
0.0, 0.0, 1.0,
x0 - x0 * cosp + y0 * sinp, y0 - x0 * sinp - y0 * cosp, 0.0)
return affine_transform(geom, matrix)
def scale(geom, xfact=1.0, yfact=1.0, zfact=1.0, origin='center'):
"""Returns a scaled geometry, scaled by factors along each dimension.
The point of origin can be a keyword 'center' for the 2D bounding box
center (default), 'centroid' for the geometry's 2D centroid, a Point
object or a coordinate tuple (x0, y0, z0).
Negative scale factors will mirror or reflect coordinates.
The general 3D affine transformation matrix for scaling is:
/ xfact 0 0 xoff \
| 0 yfact 0 yoff |
| 0 0 zfact zoff |
\ 0 0 0 1 /
where the offsets are calculated from the origin Point(x0, y0, z0):
xoff = x0 - x0 * xfact
yoff = y0 - y0 * yfact
zoff = z0 - z0 * zfact
"""
x0, y0, z0 = interpret_origin(geom, origin, 3)
matrix = (xfact, 0.0, 0.0,
0.0, yfact, 0.0,
0.0, 0.0, zfact,
x0 - x0 * xfact, y0 - y0 * yfact, z0 - z0 * zfact)
return affine_transform(geom, matrix)
def skew(geom, xs=0.0, ys=0.0, origin='center', use_radians=False):
"""Returns a skewed geometry, sheared by angles along x and y dimensions.
The shear angle can be specified in either degrees (default) or radians
by setting ``use_radians=True``.
The point of origin can be a keyword 'center' for the bounding box
center (default), 'centroid' for the geometry's centroid, a Point object
or a coordinate tuple (x0, y0).
The general 2D affine transformation matrix for skewing is:
/ 1 tan(xs) xoff \
| tan(ys) 1 yoff |
\ 0 0 1 /
where the offsets are calculated from the origin Point(x0, y0):
xoff = -y0 * tan(xs)
yoff = -x0 * tan(ys)
"""
if not use_radians: # convert from degrees
xs *= pi/180.0
ys *= pi/180.0
tanx = tan(xs)
tany = tan(ys)
if abs(tanx) < 2.5e-16:
tanx = 0.0
if abs(tany) < 2.5e-16:
tany = 0.0
x0, y0 = interpret_origin(geom, origin, 2)
matrix = (1.0, tanx, 0.0,
tany, 1.0, 0.0,
0.0, 0.0, 1.0,
-y0 * tanx, -x0 * tany, 0.0)
return affine_transform(geom, matrix)
def translate(geom, xoff=0.0, yoff=0.0, zoff=0.0):
"""Returns a translated geometry shifted by offsets along each dimension.
The general 3D affine transformation matrix for translation is:
/ 1 0 0 xoff \
| 0 1 0 yoff |
| 0 0 1 zoff |
\ 0 0 0 1 /
"""
matrix = (1.0, 0.0, 0.0,
0.0, 1.0, 0.0,
0.0, 0.0, 1.0,
xoff, yoff, zoff)
return affine_transform(geom, matrix)
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